IMO ShortList 1998, number theory problem 7
Source: IMO ShortList 1998, number theory problem 7
October 22, 2004
number theorysum of digitsDigitsDivisibilityIMO Shortlist
Problem Statement
Prove that for each positive integer , there exists a positive integer with the following properties: It has exactly digits. None of the digits is 0. It is divisible by the sum of its digits.